Sturm-Liouville Equation. Question about different forms.

[DiogenesTorch]

I have noticed the following 2 different forms for the Sturm-Liouville equation online, in different texts, and in lectures.

$[p(x) y']'+q(x)y+\lambda r(x) y = 0$

$-[p(x) y']'+q(x)y+\lambda r(x) y = 0$

Does it make a difference? I am guessing not as the negative can just be absorbed into function $p(x)$?

But I am still scratching my head as to why some texts use the negative sign in front of the 1st term. Is there some advantage to doing so?

Thanks in advance.

 

[ShayanJ]

I don't think there is much difference. In fact, I think the difference is the same as the difference between people who like to eat a special food with different sauces!

 

[DiogenesTorch]

lol the extra special sauce.

Seriously though I just wondered if somewhere the use of the negative sign has some sort of a practical reason. Like for example when solving partial differential equations using the separation of variables method, we sometimes for convenience stick a minus sign in front of eigenvalue/"separation constant."

 

[ShayanJ]

lol the extra special sauce.

Seriously though I just wondered if somewhere the use of the negative sign has some sort of a practical reason. Like for example when solving partial differential equations using the separation of variables method, we sometimes for convenience stick a minus sign in front of eigenvalue/"separation constant."

I sometimes do things with Sturm-Liouville theory and I don't put that minus sign there and never encountered a problem which can be solved by that minus sign!

 

[DiogenesTorch]

I sometimes do things with Sturm-Liouville theory and I don't put that minus sign there and never encountered a problem which can be solved by that minus sign!

Cool just wondered if it ever mattered. Thanks Shyan much appreciated :)